What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
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Rank |
Probable prime |
Digits (> 30000) |
Who ? |
When ? |
9001 | 2^180000+130153 | 54186 | Jim Fougeron | 09/2002 |
9002 | 3^113565-74 | 54185 | Lelio R Paula | 10/2012 |
9003 | 50^31891-49 | 54182 | Norbert Schneider | 07/2014 |
9004 | (5*2^179991-1)/11427 | 54180 | Lelio R Paula | 01/2014 |
9005 | 3^113548+26 | 54177 | Lelio R Paula | 10/2012 |
9006 | (lucasV(1,2,360029)-2)/(3^3*522251*725981) | 54177 | Mike Oakes | 04/2017 |
9007 | 181^23996-2 | 54176 | Lelio R Paula | 10/2017 |
9008 | 4159^14969-138 | 54173 | Enzo Doria | 07/2012 |
9010 | 2^179955+5775 | 54172 | Lelio R Paula | 10/2009 |
9009 | 2^179953-231313 | 54172 | Enzo Doria | 05/2014 |
9011 | 5^77485+6 | 54160 | Lelio R Paula | 10/2012 |
9012 | 18^43141+85 | 54154 | Lelio R Paula | 02/2013 |
9013 | 10^54149+187647 | 54150 | Patrick De Geest | 07/2017 |
9016 | 3^113489-340 | 54149 | Lelio R Paula | 10/2012 |
9014 | 10^54149-800001 | 54149 | Robert Price | 06/2017 |
9015 | 10^54149-36501 | 54149 | Patrick De Geest | 07/2017 |
9017 | 7^64070+90 | 54146 | Lelio R Paula | 10/2012 |
9018 | 12549^13210-13210^12549 | 54143 | Norbert Schneider | 12/2017 |
9019 | 18^43131+71 | 54142 | Lelio R Paula | 02/2013 |
9020 | 2^179826-131 | 54134 | Lelio R Paula | 02/2011 |
9021 | 2^179815-112735 | 54130 | Enzo Doria | 06/2014 |
9022 | 2^179806+73849 | 54127 | Enzo Doria | 04/2016 |
9023 | 2^179790+33 | 54123 | Donovan Johnson | 02/2006 |
9024 | 14287^6138+6138^14287 | 54120 | Hans Havermann | 06/2016 |
9025 | (17*10^54117+1)/9 | 54118 | Serge Batalov | 05/2010 |
9026 | 2^179763-189 | 54115 | Lelio R Paula | 02/2011 |
9027 | (21181*2^179770+1)/3029105 | 54115 | Lelio R Paula | 05/2014 |
9028 | 1828^16589+16589^1828 | 54113 | Serge Batalov | 05/2014 |
9030 | 20^41588-5883 | 54108 | Enzo Doria | 03/2013 |
9029 | 50^31847-49 | 54108 | Norbert Schneider | 07/2014 |
9031 | 2^179733-6855 | 54106 | Lelio R Paula | 10/2009 |
9032 | 20^41584-5583 | 54103 | Enzo Doria | 03/2013 |
9033 | 10^54084+3*3^54084 | 54085 | Mike Oakes | 05/2010 |
9034 | 2^179613-1795 | 54069 | Lelio R Paula | 10/2009 |
9035 | 2^179589-1011523 | 54062 | Paul Bourdelais | 11/2012 |
9036 | 2^179574-2531 | 54058 | Yves Minet | 07/2014 |
9037 | (41*10^54051-23)/9 | 54052 | Robert Price | 05/2015 |
9038 | 117^26131-116 | 54044 | Norbert Schneider | 10/2013 |
9039 | (10^54038-31)/3 | 54038 | Serge Batalov | 12/2014 |
9040 | 11^51885-84 | 54033 | Lelio R Paula | 01/2013 |
9041 | 14990^4011+4011^14990 | 54013 | Hans Havermann | 07/2016 |
9042 | (19*2^179414+1)/7 | 54010 | Lelio R Paula | 07/2012 |
9043 | 3^113182-10408 | 54002 | Enzo Doria | 02/2013 |
9044 | 35^34970-8786 | 53997 | Enzo Doria | 03/2013 |
9045 | 2^179371-1637587 | 53997 | Enzo Doria | 05/2015 |
9046 | 19^42225-92 | 53996 | Lelio R Paula | 01/2013 |
9047 | (3^113188+7)/73917675784 | 53994 | Lelio R Paula | 03/2012 |
9048 | 7*3^113162+8 | 53993 | Lelio R Paula | 03/2014 |
9049 | (10^53991+179)/9 | 53991 | Serge Batalov | 12/2014 |
9050 | 2^179350-2145 | 53990 | Lelio R Paula | 10/2009 |
9051 | (-lucasV(1,2,358718)-2)/(5*17*19) | 53990 | Mike Oakes | 04/2017 |
9052 | 8^59782-6^59782-3^59782 | 53989 | Mike Oakes | 11/2009 |
9053 | 3*7^63861+8 | 53970 | Lelio R Paula | 09/2014 |
9054 | 2^179274+71389 | 53967 | Enzo Doria | 04/2016 |
9055 | 2^179259-58695 | 53963 | Lelio R Paula | 10/2009 |
9056 | 6^69345+61 | 53961 | Lelio R Paula | 10/2012 |
9057 | (-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271) | 53957 | Mike Oakes | 04/2017 |
9058 | (40216^11719-1)/40215 | 53955 | Serge Batalov | 04/2015 |
9059 | 89*10^53951-9 | 53953 | Robert Price | 05/2017 |
9060 | 14^47067-3 | 53945 | Lelio R Paula | 01/2013 |
9061 | p(11700)#/2-512 | 53937 | Robert Price | 07/2017 |
9062 | (2^179168-5)/59 | 53934 | Lelio R Paula | 02/2012 |
9063 | 2^179128+8415 | 53923 | Lelio R Paula | 07/2012 |
9064 | 2^179120+2533 | 53921 | Henri Lifchitz | 09/2004 |
9066 | (2^179126+78557)/4649321187 | 53913 | Lelio R Paula | 05/2012 |
9065 | 74^28842+73 | 53913 | Norbert Schneider | 11/2012 |
9067 | 1271^17368+17368^1271 | 53913 | Serge Batalov | 05/2014 |
9068 | 2^179079+53 | 53909 | Lelio R Paula | 02/2011 |
9069 | 17^43807+54 | 53903 | Lelio R Paula | 01/2013 |
9070 | 17^43807+30 | 53903 | Lelio R Paula | 01/2013 |
9071 | 3^112951-310 | 53892 | Lelio R Paula | 10/2012 |
9072 | Phi(7,2957!) | 53888 | Robert Price | 05/2015 |
9073 | (10223*2^178975+1)/33985 | 53877 | Lelio R Paula | 05/2014 |
9074 | 2^178944-219209 | 53868 | Enzo Doria | 11/2012 |
9075 | (10^53859+149)/3 | 53859 | Serge Batalov | 12/2014 |
9076 | 2^178910-191 | 53858 | Lelio R Paula | 02/2011 |
9077 | 16170^2141+2141^16170 | 53857 | Hans Havermann | 07/2016 |
9078 | (5*10^53855-107)/3 | 53856 | Robert Price | 01/2017 |
9079 | (72*10^53847-27)/99 | 53847 | Patrick De Geest | 08/2004 |
9080 | 2^178841-869688105 | 53837 | Lelio R Paula | 06/2012 |
9081 | 2*10^53834-27 | 53835 | Robert Price | 02/2017 |
9083 | 2^178821-1011523 | 53831 | Paul Bourdelais | 11/2012 |
9082 | 12601^13128-13128^12601 | 53831 | Norbert Schneider | 10/2017 |
9084 | 2^178819-15 | 53830 | Lelio R Paula | 02/2011 |
9085 | (14450!-1)/225296581 | 53829 | Donovan Johnson | 04/2006 |
9086 | (124351#+125386)/(2^5*71*883*4489103*9820259) | 53826 | Makoto Morimoto | 10/2017 |
9087 | 10530^13381-13381^10530 | 53825 | Norbert Schneider | 03/2018 |
9088 | 2^178761-465 | 53813 | Lelio R Paula | 10/2009 |
9089 | 18900^703+703^18900 | 53808 | Anatoly F. Selevich | 02/2007 |
9090 | 13918^7343+7343^13918 | 53806 | Hans Havermann | 08/2016 |
9091 | 10^53804+31749 | 53805 | Patrick De Geest | 12/2012 |
9092 | 10^53804-71 | 53804 | Robert Price | 05/2011 |
9093 | t(178994) | 53804 | Robert Price | 03/2015 |
9094 | (2^178693-lucasV(1,2,178693)+1)/2 | 53792 | Mike Oakes | 11/2016 |
9095 | 2^178671-113215 | 53786 | Enzo Doria | 07/2014 |
9096 | 15110^3621+3621^15110 | 53774 | Hans Havermann | 07/2016 |
9097 | 2^178611+95 | 53768 | Lelio R Paula | 02/2011 |
9098 | 2^178597+5711 | 53764 | Lelio R Paula | 10/2011 |
9099 | 2^178598+12915 | 53764 | Lelio R Paula | 07/2012 |
9100 | (9179*2^178579-1)/303 | 53760 | Lelio R Paula | 03/2015 |
9101 | 10671^13342-13342^10671 | 53745 | Norbert Schneider | 02/2018 |
9102 | 5*7^63589+2 | 53740 | Lelio R Paula | 09/2014 |
9103 | 2^178516-112515 | 53739 | Enzo Doria | 06/2014 |
9104 | 20^41302-27 | 53736 | Lelio R Paula | 01/2013 |
9105 | 6^69054-39209 | 53735 | Mike Oakes | 12/2010 |
9106 | 13086^12769+12769^13086 | 53734 | Hans Havermann | 07/2016 |
9107 | 2^178455+76043 | 53721 | Enzo Doria | 04/2016 |
9108 | (10^53718-7)/3 | 53718 | Makoto Kamada | 10/2004 |
9109 | (67607*2^178426+1)/3 | 53716 | Lelio R Paula | 05/2014 |
9110 | 9*10^53707+11 | 53708 | Robert Kinser | 01/2017 |
9111 | 94601!8-2 | 53708 | Robert Price | 04/2017 |
9112 | 13214^11595+11595^13214 | 53706 | Hans Havermann | 07/2016 |
9113 | Phi(134350,10)/537401/8011962251 | 53705 | Maksym Voznyy | 10/2011 |
9114 | 2^178367-379 | 53694 | Yves Minet | 03/2013 |
9115 | (2^178364-5)/11 | 53692 | Lelio R Paula | 02/2012 |
9116 | 4339^14760-168 | 53688 | Enzo Doria | 06/2012 |
9117 | 12^49746-11 | 53685 | Lelio R Paula | 01/2013 |
9118 | 12950^13051-13051^12950 | 53670 | Norbert Schneider | 08/2017 |
9119 | (9913*2^178266-1)/2247 | 53665 | Lelio R Paula | 03/2015 |
9120 | 13725^8128+8128^13725 | 53665 | Hans Havermann | 07/2016 |
9121 | 2^178250-113261 | 53659 | Enzo Doria | 07/2014 |
9122 | 2^178226+11715 | 53652 | Lelio R Paula | 10/2009 |
9123 | 35^34742-1976 | 53645 | Enzo Doria | 03/2013 |
9124 | 20^41228-563 | 53639 | Enzo Doria | 03/2013 |
9125 | 359^20992+20992^359 | 53637 | Norbert Schneider | 08/2014 |
9126 | (27*2^178183-1)/29065 | 53636 | Lelio R Paula | 01/2014 |
9127 | (3^112414+7)/37381696 | 53628 | Lelio R Paula | 03/2012 |
9128 | 17994^955+955^17994 | 53623 | Anatoly F. Selevich | 10/2006 |
9129 | 2^178117-1551 | 53619 | Yves Minet | 08/2012 |
9130 | 2^178099-11287 | 53614 | Enzo Doria | 06/2014 |
9131 | 10751^13298-13298^10751 | 53611 | Norbert Schneider | 01/2018 |
9132 | (15*2^178080-1)/309071 | 53604 | Lelio R Paula | 01/2014 |
9133 | 5^76672-13766 | 53592 | Enzo Doria | 02/2013 |
9134 | 6^68868-137 | 53590 | Lelio R Paula | 10/2012 |
9135 | (5*2^178021+1)/8173 | 53587 | Lelio R Paula | 07/2012 |
9136 | 5^76654-26 | 53579 | Lelio R Paula | 10/2012 |
9137 | (3^112297-2)/7627 | 53576 | Lelio R Paula | 03/2012 |
9138 | 3*2^177948-7 | 53569 | Lelio R Paula | 03/2014 |
9139 | 10^53558+18543 | 53559 | Patrick De Geest | 12/2012 |
9140 | 10^53558-21 | 53558 | Robert Price | 03/2011 |
9141 | 2^177792-95 | 53521 | Lelio R Paula | 02/2011 |
9142 | 13392^9919+9919^13392 | 53521 | Hans Havermann | 07/2016 |
9143 | 13105^12132+12132^13105 | 53520 | Hans Havermann | 07/2016 |
9144 | 13^48042+82 | 53517 | Lelio R Paula | 01/2013 |
9145 | 2^177768+39121 | 53514 | Yves Minet | 10/2010 |
9146 | 13835^7366+7366^13835 | 53504 | Hans Havermann | 07/2016 |
9147 | 17^43477+84 | 53497 | Lelio R Paula | 01/2013 |
9148 | 5*10^53492+9 | 53493 | Dmitry Domanov | 11/2010 |
9149 | 2^177683+95 | 53488 | Lelio R Paula | 01/2011 |
9150 | 11057^13226-13226^11057 | 53482 | Norbert Schneider | 12/2017 |
9151 | (2^177678+3)/514627 | 53481 | Lelio R Paula | 02/2012 |
9152 | 2^177641-255463 | 53476 | Gary Barnes | 08/2009 |
9153 | p(11608)#/2+16 | 53469 | Robert Price | 12/2016 |
9154 | (14*10^53465+211)/9 | 53466 | Robert Price | 11/2017 |
9155 | 37302#*10^(37302+52)+p(37302+1) | 53457 | Jason Earls | 08/2008 |
9156 | 12001^13104-13104^12001 | 53455 | Norbert Schneider | 10/2017 |
9157 | 1829^16384+1828^16384 | 53449 | Henri Lifchitz | 01/2007 |
9158 | 35^34608-9602 | 53438 | Enzo Doria | 03/2013 |
9159 | (3^111992+8)/14867 | 53430 | Lelio R Paula | 03/2012 |
9161 | 2^177480+1869661 | 53427 | Enzo Doria | 05/2016 |
9160 | 11791^13122-13122^11791 | 53427 | Norbert Schneider | 10/2017 |
9162 | (8*10^53411+1)/9 | 53411 | Serge Batalov | 12/2008 |
9163 | 4*5^76410-3 | 53409 | Lelio R Paula | 09/2014 |
9164 | 2^177380-113045 | 53397 | Enzo Doria | 07/2014 |
9165 | 5^76362-2*3^76362 | 53375 | Mike Oakes | 11/2009 |
9166 | 4159^14747-140 | 53370 | Enzo Doria | 07/2012 |
9167 | (lucasV(1,2,354503)-2)/3 | 53358 | Mike Oakes | 03/2017 |
9168 | p(11586)#/2+32 | 53357 | Robert Price | 12/2016 |
9169 | 15^45362-46 | 53350 | Lelio R Paula | 01/2013 |
9170 | 14147^5892+5892^14147 | 53338 | Hans Havermann | 07/2016 |
9171 | 7^63109+46 | 53334 | Lelio R Paula | 10/2012 |
9172 | 20^40986-1343 | 53325 | Enzo Doria | 03/2013 |
9173 | 4*10^53324-89 | 53325 | Robert Price | 08/2017 |
9174 | 20^40977-8883 | 53313 | Enzo Doria | 03/2013 |
9175 | 3^111711+2660 | 53300 | Lelio R Paula | 10/2012 |
9176 | 2^177040-11865 | 53295 | Enzo Doria | 10/2012 |
9177 | (7*10^53287+17)/3 | 53288 | Erik Branger | 03/2014 |
9178 | 35^34506-10758 | 53280 | Enzo Doria | 03/2013 |
9179 | (11*10^53274-17)/3 | 53275 | Erik Branger | 03/2014 |
9180 | (1017*2^176971-1)/335 | 53275 | Lelio R Paula | 03/2015 |
9181 | 2^176961-2833 | 53271 | Yves Minet | 09/2014 |
9182 | 3^111642+110 | 53267 | Lelio R Paula | 10/2012 |
9183 | 17^43290-98 | 53267 | Lelio R Paula | 01/2013 |
9184 | 7^63028+36 | 53265 | Lelio R Paula | 10/2012 |
9185 | (22*10^53264+71)/3 | 53265 | Robert Price | 05/2017 |
9186 | 7^63023-36 | 53261 | Lelio R Paula | 10/2012 |
9187 | 19783^492+492^19783 | 53256 | Anatoly F. Selevich | 02/2007 |
9188 | 13350^9739+9739^13350 | 53247 | Hans Havermann | 10/2015 |
9189 | 14394^4993+4993^14394 | 53235 | Hans Havermann | 10/2015 |
9190 | 2^176823-112807 | 53230 | Enzo Doria | 06/2014 |
9191 | 1684^16495+16495^1684 | 53219 | Serge Batalov | 05/2014 |
9192 | 15277^3042+3042^15277 | 53213 | Hans Havermann | 06/2016 |
9193 | (50322^11317-1)/50321 | 53206 | Serge Batalov | 04/2015 |
9194 | 2^176742-1595 | 53205 | Lelio R Paula | 10/2009 |
9195 | (27*2^176767-1)/20455056355 | 53204 | Lelio R Paula | 01/2014 |
9196 | (-lucasV(1,2,353460)-2)/(3^2*5^2) | 53199 | Mike Oakes | 03/2017 |
9197 | (3*2^176696-1)/299 | 53189 | Lelio R Paula | 01/2014 |
9198 | (7*10^53185-1)/3 | 53186 | Erik Branger | 03/2014 |
9199 | 2^176629+465 | 53171 | Lelio R Paula | 07/2012 |
9200 | (3*2^176604-1)/359 | 53162 | Lelio R Paula | 01/2014 |
9201 | 10955^13158-13158^10955 | 53154 | Norbert Schneider | 11/2017 |
9202 | 5^76038-14366 | 53149 | Enzo Doria | 02/2013 |
9203 | 15156^3209+3209^15156 | 53143 | Hans Havermann | 06/2016 |
9204 | 2^176532-2837 | 53142 | Yves Minet | 09/2014 |
9205 | 52^30967-51 | 53140 | Norbert Schneider | 08/2014 |
9206 | 9*5^76023-2 | 53139 | Lelio R Paula | 09/2014 |
9207 | (14283!+1)/464216177 | 53135 | Michael Porter | 03/2016 |
9208 | 2^176461-165 | 53121 | Lelio R Paula | 02/2011 |
9209 | (62*10^53111+1)/9 | 53112 | Serge Batalov | 05/2010 |
9210 | 2^176403-139 | 53103 | Lelio R Paula | 02/2011 |
9211 | 55^30508-2 | 53095 | Lelio R Paula | 08/2013 |
9212 | (48591^11329-1)/48590 | 53090 | Serge Batalov | 04/2015 |
9213 | 3^111254-88 | 53082 | Lelio R Paula | 10/2012 |
9214 | 15^45129-56 | 53076 | Lelio R Paula | 01/2013 |
9215 | 2^176293-73 | 53070 | Lelio R Paula | 01/2011 |
9216 | (67*10^53068+41)/9 | 53069 | Robert Price | 09/2015 |
9217 | 15271^2986+2986^15271 | 53069 | Hans Havermann | 06/2016 |
9218 | 2^176255-667 | 53059 | Yves Minet | 01/2012 |
9219 | 36471*2^176221+8647 | 53053 | Paul Vanderveen | 04/2016 |
9220 | (19*10^53049-1)/9 | 53050 | Serge Batalov | 03/2009 |
9221 | 9*2^176203-5 | 53044 | Lelio R Paula | 03/2014 |
9222 | 2^176205-94395 | 53043 | Lelio R Paula | 08/2011 |
9223 | (19*2^176224-1)/217916913 | 53042 | Lelio R Paula | 01/2014 |
9224 | 17^43103+14 | 53037 | Lelio R Paula | 01/2013 |
9225 | (31*2^176188-1)/3555 | 53036 | Lelio R Paula | 01/2014 |
9226 | 2^176177+60947 | 53035 | David Broadhurst | 05/2002 |
9227 | (22*10^53033-7)/3 | 53034 | Erik Branger | 09/2014 |
9228 | 13810^6909+6909^13810 | 53023 | Hans Havermann | 06/2016 |
9229 | 2^176108+16095 | 53014 | Lelio R Paula | 10/2009 |
9230 | 2^176107+18915 | 53014 | Lelio R Paula | 07/2012 |
9231 | 3^111080-9628 | 52999 | Enzo Doria | 02/2013 |
9232 | 2^176047-1551 | 52996 | Yves Minet | 08/2012 |
9233 | 2^176042+73519 | 52994 | Enzo Doria | 04/2016 |
9234 | lucasV(1715,1,2^14)/65537 | 52986 | Mike Oakes | 04/2009 |
9235 | 2^175984-112259 | 52977 | Enzo Doria | 06/2014 |
9236 | 11^50870+10 | 52976 | Lelio R Paula | 01/2013 |
9237 | (11*10^52956+19)/3 | 52957 | Robert Price | 03/2016 |
9238 | gcd(V(949965),5*F(189993)*(F(189993)+1)+1) | 52941 | Serge Batalov | 04/2015 |
9239 | (-lucasV(1,2,351735)+2)/(3*7*263) | 52938 | Mike Oakes | 03/2017 |
9241 | (98*10^52931-89)/99 | 52931 | Ray Chandler | 11/2010 |
9240 | 13774^6963+6963^13774 | 52931 | Hans Havermann | 06/2016 |
9242 | 2^175812-1367 | 52925 | Yves Minet | 05/2013 |
9243 | 2^175801+1155*175801 | 52922 | Henri Lifchitz | 01/2005 |
9244 | 11^50801-9090 | 52904 | Enzo Doria | 02/2013 |
9245 | 43^32374+12 | 52882 | Robert Price | 11/2013 |
9246 | 2^175628+13 | 52870 | Lelio R Paula | 01/2011 |
9247 | 2^175615-1747 | 52866 | Yves Minet | 09/2012 |
9248 | (13*10^52861+107)/3 | 52862 | Robert Price | 11/2017 |
9249 | 9*2^175586-7 | 52858 | Lelio R Paula | 03/2014 |
9250 | 12174^12937+12937^12174 | 52854 | Norbert Schneider | 04/2016 |